Writer and Television Producer; Author, Remembering Our Childhood: How Memory Betrays Us

Would an extra-terrestrial civilization develop the same mathematics as ours? If not, how could theirs possibly be different?

In writing my next book, about maths, I have been led to ponder this question by the fact that there are philosophers, and a few mathematicians, who believe that it is conceivable that there could be intelligences with a fully developed mathematics that does not, for example, recognize the integers or the primes, let alone Fermat's Last Theorem or the Riemann Hypothesis. And yet, whole numbers seem to us such a basic property of "things", that unless there were intelligences that were not embodied in any way (and/or couldn't "see" the discrete stars, for example) they would be bound to come across number and all that follows. But then, I suppose you could imagine intelligent beings which consisted, say, of density differences in a gas but lacked boundaries separating one from another. In any case, if such creatures do exist, it rather pours cold water on the use by SETI of maths (e.g. prime x prime pictorial grids) to communicate with them